Inertia

Galileo observed that objects ‘resist’ changes to their motion.

• If an object is at rest it resists efforts to start it moving,

• If an object is moving it resists efforts to change its velocity.

• The motion can be linear motion, rotational motion, vibrational motion.

We call this property an object’s inertia. For motion in a straight line – linear motion – the inertia of an object is the same as its mass.

Newton’s First Law is sometimes called The Law of Inertia.

Newton's Second Law of Motion

Newton's First Law implies force is related to acceleration but it does not state what that relationship is. From observation, we find:

• the acceleration is in the same direction as the force,

• the size of the acceleration is proportional to the size of the force,

• the acceleration is inversely proportional to the object's inertia. Newton's Second Law states:

The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to the object's mass. The direction of the acceleration is in the direction of the net force acting on the object.

In mathematical terms:

• a= F_net/m

  • Remember F_net is the vector sum of all the forces.

The SI unit of force is the newton – symbol N. One newton is the amount of force required to accelerate an object of mass 1 kg by 1 m/s^2 .

To use Newton’s 2nd Law we need to compute the net force. Sometimes the forces are not all along the same line. The forces have to be broken down into components.

The components of the forces in the y direction cancel leaving just the component of FP in the horizontal direction. The box accelerates in the x direction even though none of the forces point in this direction.

Mass

• Newton's Second Law allows us to define mass.

  • the mass of an object is the constant (scalar) of proportionality between a net force upon an object and the acceleration of the object.

• The unit of mass used to be that of an object – the prototype kg.

  • the definition of the kg changed in May 2019.

• The mass of any other object can be determined by comparing the accelerations to the same applied force.

• As we learned, close to Earth Galileo observed the acceleration due to gravity was the same for all objects.

  • If there are no other forces acting on an object except gravity we know the acceleration - g

• The gravitational force on an object near Earth is

  • F_G=mg

  • For a long time physicists distinguished between two different masses – gravitational mass (the mass that causes the attraction of other objects via gravity) and inertial mass (the mass that enters Newton’s 2nd Law).

    • There are even two gravitational masses – passive and active.

    • Experimentally they are all equal.

    • Einstein’s theory of General Relativity is built upon the assumption that gravitational and inertial mass are the same – Equivalence Principle.

QUESTION 1:

On Earth Neil Armstrong’s mass was 80 kg. When he went to the Moon, how did his mass compare?

• His mass remained the same since mass never changed, only weight can change.

QUESTION 2:

On Earth Neil Armstrong’s weight was 800 N. When he went to the Moon, how did his weight compare?

• His weight was less on the Moon because the gravity is less there.

QUESTION 3:

On Earth astronaut Christina Koch’s weight is 600 N. When she was on the International Space Station, was her weight zero?

• No, weight can never be zero.

Friction

Friction is the force that opposes motion. There are two basic 'types' of friction.

• kinetic friction – the force upon two objects which are in contact and in relative motion which opposes the relative motion.

  • Kinetic friction is a force directed opposite the velocity. Experiment shows the size of the kinetic friction force is proportional to the size of the normal force.

• static friction – the force upon two objects which are in contact and not in relative motion and which opposes any relative motion. The study of friction is called Tribology.

  • There can be friction between two objects even though they are not moving relative to each other. This kind of friction is called static friction. The size of the static friction is not fixed: it is as big as it needs to be to oppose relative motion, up to some maximum.

  • If the static friction necessary to prevent motion is larger than the maximum, the object cannot remain at rest and the friction will then become kinetic friction. Experiment shows the maximum size of the static friction force is proportional to the size of the normal force.

If an object ‘rolls’ upon another without slipping, there is a different kind of friction between them called rolling friction.

• Like kinetic friction, rolling friction is a fixed size and it points opposite the relative velocity between the two objects. Rolling friction is usually negligible.

For both static and kinetic friction, the amount of friction depends upon the two materials in contact.

• The friction between steel ball with a mass of 1 kg on ice is much less than between rubber ball of mass 1 kg and an asphalt road.

• The friction does not depend upon the area of the contact between the two objects.

• Kinetic friction doesn’t depend upon the speed.

Drag Forces

When an object moves through a fluid such as air or water, the fluid exerts a drag force upon the object.

• when the fluid is air the drag force is sometimes known as air resistance.

Unlike friction, the drag force depends upon:

• the shape / size of the object,

• the speed of the object (unlike kinetic friction),

It also depends on the properties of the fluid such as its viscosity and density,

• The drag force on an object of a given speed as it moves through molasses is much higher than if it moves at that speed through water.

At low speeds the drag force is proportional to the speed.

• sometimes called Stoke’s drag or laminar drag

At high speeds the drag force is proportional to the square of the speed.

• sometimes called Newton’s drag or turbulent drag

Terminal Speed (Velocity)

Consider an object falling down through air i.e. it is subject to air resistance R. The net force is Fnet = mg – R so the acceleration of the object is:

• a= 1/m (mg−R)= g−R/m

• The object’s acceleration is still downward but it’s less than g.

  • The objects speed keeps increasing. As the speed increases, the drag force R increases. When the object reaches the terminal speed the air resistance force cancels the force of gravity so a = 0.

• no acceleration → no change in speed

The larger the mass the higher the terminal speed (everything else being equal): it takes a larger R to cancel the mg.

QUESTION 1:

As a skydiver falls faster and faster through the air, air resistance

• A. increases.

• B. decreases.

• C. remains the same.

• D. Not enough information.

A. increases

QUESTION 2:

As a skydiver continues to fall faster and faster through the air, net force

• A. increases.

• B. decreases.

• C. remains the same.

• D. Not enough information.

B. decreases

CHAPTER 5

Newton's Third Law of Motion

If an object accelerates, the net force applied to the object (of constant mass), must come from an external agent. Consider two objects A and B.

• A exerts a force on B causing B to accelerate,

• B exerts a force on A causing A to accelerate,

• But the combination of A and B does not accelerate

A single object, or a system of objects, of constant mass cannot cause its own acceleration.

Newton's Third Law of Motion states:

Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.

The two forces are often called an ‘action-reaction’ pair.

QUESTION 1:

A soccer player kicks a ball with 1500 N of force. What is the force on the player's foot?

• 1500 N

QUESTION 2:

Consider a high-speed bus colliding head-on with a flying bug. The force of impact splatters the unfortunate bug over the windshield. Which is greater, the force on the bug or the force on the bus?

• It’s the same. Although the forces are equal in magnitude, the effects are very different because the accelerations are very different.

QUESTION 3:

You measure your weight – the gravitational force of the Earth on you – and find it is 700 N and it points down. What is the force on the Earth due to you?

• 700 N and up.